Motorized Bikes

A motorized bicycle is different from a motorcycle in that the engine or motor has much less horsepower.  If it meets a few rules no license is needed for the bike or rider.  The fuel economy can be quite good. Another name for them is moped.  Also see my Bicycle Science, 3 Wheel Recumbent Electric Bikes, Tilting Three Wheeler & Vehicles web page

Three Wheels

Steering stability that has to do with slip angles and over vs. under steer.  With a single front wheel on a three wheel vehicle the steering is considered unstable because when it drifts in over steer the rear end tends to get in front of the front.

Rollover stability has to do with the location of the c.g. relative the the tire contact patches.

The Tri Hawk could no be rolled over on smooth asphalt so has good roll over stability and has front wheel steering so has good steering stability.  The Morgans on the other hand have front wheel steering, but a high c.g. so tend to roll over in a hard turn.

Two Wheels

The stability of a two wheel vehicle is a function of it's road speed and effective design.  "Effective design" is the design including the effects of construction and maintenance, for example if bearings are worn then the bearing slop is part of the "effective design".

Bicycle

Delft Bicycle Dynamics Lab - design equations for a two wheeled vehicle where the major components are assumed to be rigid and no tire properties are included.  This limited analysis does allow some stability parameters to be calculated. 
06PA0459BicyclePaperv45.pdf - "Linearized dynamic equations for the balance and steer of a bicycle and steer of a bicycle: a benchmark and review"
Four parts make up the model: Front Wheel, Rear Wheel, Rear Frame including the rider, Front Fork including Handlebar
For the reference design given in the paper the following stability factors are present::
At near zero speed 9, 0.5 m/s) the bicycle stability is like an upside down pendulum and can fall over to the left or right.
Next  (0.7 to 4.3 m/s) comes the weave unstability where the bick steers left right left etc.
Nex (4.3 to 6 m/s) the bike is self stable (it will roll without falling over without a rider.  6 m/s is called the capsize speed and above this speed the bike is marginally stable.

Motorized Bicycle

The classic example is the Wizzer (see below).
But you can still buy kits to add a 50cc (U.S. definition of displacement) / 80cc (China definition of displacement plus head volume) motor kits for bicycles.
I live in a hilly location and the slope of my drive way is over 11% (Wiki) and this motorized bicycle was able to drive up to the top.
That's really doing something that most electric bikes can not do.
One seller is Fast Bike Motors, but there are plenty just search for "motorized bicycle".
The Bicycle shown below is a Northrock CTM which is sold at Costco.  Because it has a large diameter down tube where the motor mount is located it might pay to get the optional motor mount bracket from Fast Bike Motors.

MotoPed

Appears to be a kit of parts including a patent pending jack-shaft system.  Uses horizontal E-22 (Honda style) engines up to 155cc (MotoPed: FAQ).  When the 49cc engine is used it's probably in the unlicensed category of a motorbike.

Part of Motovox and tied to SmartCarb (will increase the fuel economy by an additional 25% to 40% with a target of 200+ miles per gallon, but costs about $700 so not economical).

$2,000 for a kit missing the engine and a few other items, or about $3,000 assembled and ready to ride.
Gross Vehicle Weight is not specified. Dry weight just over 120 pounds and varies a little with the model.

Phantom Bikes - no license, not registration, no drivers license, maybe need a helmet.  Although the bikes shown on the Jay Leno Garage video were powered by a 49cc gas engine, the bikes shown on their web page seem to be all electric.

bicycle-engines.com - has 2-cycle and 4-cycle kits as well as various parts.

Honda Cub (Wiki, Quora: What is the best all around motorcycle? Why?)

While made to be a motor bike rather than a conversion I put it under Motorized Bicycle rather than Motor Scooter because it has larger diameter wheels.  A very important distinction because of the greater stability related to gyroscopic effects.

The Wiki page says the Super Cub is the Most produced motor vehicle in history.  The early versions and some current versions have 49cc engines so that in many locations there's no licensing required.

Here's the official Honda web page for the: 2021 Super Cub C125, labeled "The World's Favorite Bike".
Fuelly reports that the C125A gets about 116 MPG with a range of 100 to 139 MPG.
Topspeed reports: 60 MPH

Motor Scooter

I'm writing this while in Taiwan where motor scooters outnumber cars and maybe even the population.  There are a very small number of light motorcycles and I haven't seen any heavy motorcycles.  The reason is the very congested traffic.  Motor scooters have a number of advantages when compared to everything else:

• the front apron protects your lower body from being hit by insects and rain when in motion
•  "     "        " and the rear mounted engine/transmission act as bumpers to protect your legs if you are sideswiped or trapped between two cars unlike a motorcycle
•  "     "        " provides for some modesty for female drivers wearing skirts and allows them to ride without straddling like on a motorcycle
  
• the flat floor can be used to hold cargo, a dog, or whatever
• the closable storage compartment (some with a lock) holds things you want to be out of sight like a helmet or other valuables
• add on storage compartments and racks are available
• there is a passenger seat with associated foot rests to carry someone else
• The small wheels allow maneuvering in tight places where a motorcycle could not be operated
•  "       "         "      have much less gyroscopic stability than motorcycle wheels and so a scooter may flip over if driven over angled tracks or joints
  
• the continuously variable transmission means there's no shifting which is very handy in city stop and go traffic
• typically much lighter than motorcycles
• in Taiwan there are special provisions for motor scooters like separate lanes, waiting spaces at traffic lights in front of the line for cars, etc.
• much easier to park than a car (like on the sidewalk)
• most cities have a number of small shops the sell - repair scooters
• very good gas mileage (80 + miles/gallon)
• the seat is low enough so that you can rest your feet on the ground when stopped

Common Scooter Brands in Taiwan:

Kymco (Kwang Yang Motor Co)-
Liado
PGO - Motive Power Industry associated with Piaggio of Italy
Sanyang Industry Co (SYM), Taiwan - Whizzer - although the Whizzer is made in Taiwan they are not popular there.

Yamaha - has a scooter R&D operation in Taiwan.

Sources of motive power

2SG 2-stroke gas

4SG 4-stroke gas

EM electric motor

Vehicle type

Sct scooters

BK bicycle add on kit

Gas (Kit or Purpose Built)

PMB purpose made bicycles

LM light motorcycles

Motive Drive Location

IFW inside the front wheel

AFW above the front wheel

Frm between the front and seat frame tubes

MID replaces the crank cartridge

ARW above the rear wheel

IRW inside rear wheel

BRW behind rear wheel

Maker	Model	Description	Pwr	Type	Drv Loc
Cushman
eZee
Wizzer	all	gas engine ki	2SG	BK PMB	Frm
Zap	DX	Dual Motor Kit	EM	BK	FRW
Zap	SX	Single Motor Kit	EM	BK	FRW

703695 Gas Engine, Everett B. Cushman & Leslie S. Cushman (Cushman Motor Works), Oct 26, 1901, 123/73A ; 123/65A; 123/73V
721287 Packing for Engines, Leslie S. Cushman & Everett B. Cushman (Cushman Motor Works), Feb 24, 1903, 277/385 ; 123/73R; 277/397; 384/135; 384/142
736224 Gas Engine, Everett B. Cushman & Leslie S. Cushman (Cushman Motor Works), Aug 11, 1903,
794927 Carburetor, Everett B. Cushman & Leslie S. Cushman (Cushman Motor Works), Jul 18, 1905, 261/51 ; 261/52; 261/58; 261/70
858707 Gas-Engine, Leslie S. Cushman & Everett B. Cushman (not assigned), Jul 2, 1907, 123/73A ; 123/73V
861438 Carburetor, Everett B. Cushman & Leslie S. Cushman (Cushman Motor Works), Jul 30, 1907, 261/64.4 ; 137/527; 261/63
1008309 Friction Clutch, Everett B. Cushman (not assigned), Nov 14 1911, 192/93A ; 192/89.21
1099916 Splash Lubricating System, Everett B. Cushman (Cushman Motor Works), Jun 16 1914, 184/11.2 ; 184/11.1; 184/6.24
1289404 Water-cooler for Engines, Everett B. Cushman (not assigned), Dec 31, 1918, 123/41.52
1347685 Splash Lubricating System, Everett B. Cushman (not assigned), Jul 27, 1920, 184/13.1
1369327 Oil-feeder, Everett B. Cushman (Piersen Mfg), Feb 22, 1921, 184/103.2 ; 137/435; 137/437; 137/453
1375748 Automatic Oil-feed, Everett B. Cushman (Piersen Mfg), Apr 26, 1921, 184/103.2 - crankcase
1391668 Clutch, Everett B. Cushman (Piersen Mfg), Sep 27 1921, 192/70.27 ; 192/89.27
1417037 Radiator, Everett B. Cushman (Piersen Mfg), May 23 1922, 165/86 ; 123/41.44; 165/125; 165/92; 165/DIG.147
1630527 Internal-combustion Engine, Everett B. Cushman (not assigned), May 31, 1927, 123/286 ; 123/263; 123/265; 123/41.72
2274043 Motorized Bicycle, Leslie S. Cushman (not assigned), Feb 24, 1942, 180/221 ; 180/205 -
2429153 Centrifugal Clutch, Charles D. Ammon (Cushman Motor Works), Oct 14 1947, 192/105CD ; 180/219; 192/109R; 74/333
2556512 Variable Ratio Drive Mechanism, Charles D. Ammon (Cushman Motor Works), Jun 12 1951, 474/14 -

2601342 Mounting for Internal-combustion Engines, A. Starts (Camfield), Jun 24 1952, 180/222 ; 15/88.3; 477/34

500  to 3,000 RPM output is between 6.0 and 7.2 Volts
References:
  578280 Dynamo Electric Machine and Electric Motor, CHARLES P. TURNER, Mar 2, 1897, 310/254 ; 310/218 -
1137544 Tone Producing Means, Severy, Apr 27 1915, 84/19 ; 310/111; 310/155; 310/191 - musicaltone generator using disks with various shapes
1904308 Magneto, KENNETH A. HARMON (WICO ELEC), Apr 18, 1933, 310/153 ; 123/634; 310/155 -
1977600 Electromagnetic Pole, Anthony Winther, Oct 16 1934, 310/105 ; 310/218 - Eddy current electric clutch
2071573 Ignition System, Randolph (GM corp), Feb 23 1937,
2081800 Magneto-Electric Generator, Le Roy S. Dunham (Edison-Splitdorf corp), May 25, 1937, 310/156.51 ; 310/156.11; 310/261 -
2104707 Electric Generator, William Rawlings, Jan 4 1938, 310/66 ; 310/156.18; 310/156.26; 310/67A; 310/67R -
2213724 Magneto Rotor, Edward A. Vogel (Fair-banks Morse & co), Sep 3 1940, 310/156.23 ; 310/156.14; 310/42 - PM mounting
2248030 Motion Transmitting Mechanism, Zwack, July 1, 1941, 310/104 ; 310/97; 417/420; 73/861.75 - magnetically coupled
2489517 Magnetoelectric Machines, William Brown, Nov 29, 1949, 310/75C ; 310/90

multiple tubes for a stronger frame - looks very much like the Schwinn 2151533
References:
2151533 Bicycle Frame, Frank W. Schwinn, Mar 21 1939, 280/281.1 ; D12/111
2250805 Bicycle, George Lewiaski (Hettrick Mfg), Jul 29 1941, 280/288 - oval with no internal brace.
2280801 Bicycle Construction, awrence E. Dempsey (Sears Roebuck & Co), Apr 28, 1942, 280/284 -

a counter shaft has two pulleys on a common shaft.  Moving the shaft closer to the engine allows belt slip.  Not really a variable drive but just slip.
References:
  355555 Pulley, Radford, Jan 4 1887, 474/182 ; 474/903 - made from two spun or spamped sheetmetal disks
  718084 Generating Alternating Currents, CHARLES S. BRADLEY (GE),
  729197 Motor Cycle Gear, EUGENE MATHIEU, May 26 1903, 474/89 ; 180/205; 180/231 - chain drive that can be disengaged
  833979 Shafting, HENRY K. SANDELL (MILLS NOVELTY CO), Oct 23, 1906, 474/89 ; 112/270 - idler pulley system
1978526 Driving Mechanism, Eppler (United Shoe Machinery corp), Oct 30 1934, 474/89 ; 15/390 - over center idler pulley
2047362 Pulley Belt Control Device, Ernest Dunford (Landis Machine Co), Jul 14, 1936, 474/133 - V belt idler - disconnector
2156701 Belt Drive Mechanism, Thorvald Peterson (R F Wright), May 2, 1939, 474/114 ; 298/35R; 474/140 - electric motor on hinged plate

Improved large pully for attachment to rear wheel spokes that's centered and stays centered.
References:
718094 Wheel for Motor Cycles, A. Clement, Jan 13 1903, 301/6.5 ; 301/55 - large pulley on rear wheel clamps to spokes and has it's own spoke to rim.
1062905 Screw-Spikes, Gadd, May 1913 - for holding railroad rails
1186224 Metal Vehicle Wheel, T.E. Murray, Jun 6 1916, 301/6.7 ; 188/218R - includes brake drum
1355505 Wheel Construction, JOHN KIISK, Oct 12, 1920, 301/6.7 ; 301/104 - matal bands instead of spokes & brake drum
1561180 Attaching Means for use on Wire Spoke Wheels, JOSEPH F. MERKEL (GRS Products), Nov 10, 1925, 74/432 ; 301/6.7 -
1618074 Pulley, ARTHUE M. PLORY, Feb 15, 1927, 74/15 ; 301/40.5; 301/6.7; 474/47 - mounts to wood spoked wheel

References:
1360165 Method for Making Commutators, CHARLES C. ZENK (Diehl Mfg), Nov 23, 1920, 264/261 ; 264/277; 29/597; 310/235 -
1360166 Method for Making Commutators, CHARLES C. ZENK (Diehl Mfg), Nov 23, 1920,
1898929 Commutator and Method of Making it, V.G. Apple, Feb 21 1933, 310/235 ; 264/272.2; 29/597
1991046 ROCESS FOB MAKING MAGNETO ROTORS, Jakob Bohli, Feb 12, 1935, 310/156.51 ; 29/598; 310/156.23; 310/42
2468146 Cigarette Lighter, Vissing, Apr 26, 1949, 219/268 ; 310/69; 310/75A - small electric generator heats wire
2475776 ROTOR FOR DYNAMOELECTRIC MACHINES, Maurice W. Brainard, Jan 12 1947, 310/156.76 ; 310/269 - PM type
2516901 ROTOR FOR DYNAMOELECTRIC MACHINES, Wayne J. Morrill, Aug 1 1950, 310/156.18 

References:
1949962
2280734
2329525
2448436
2468894
2499750

These are a step up, they are classified as motorcycles.  The idea is to have the stability of a 4 wheel vehicle but keep the overhead costs down in the motorcycle area.

205 With mechanism of occupant-powered type for developing torque for supplementing, alternating with, or replacing torque of motor